Can Blender use a GPU's remotely? (over a network)
No, there is currently to have a local Blender instance access a remote GPU to make use of it from Cycles. *

There is a network-rendering component to Cycles however this isn't ready for production use, and nobody is actively developing it.

Alternatives:


Use a render farm (send your files to the server).
Use a remote-desktop login to the faster system (using standard remote desktop access).


... though realistically you may be better off to get a computer that supports swapping out graphics cards.



* Probably this has done under some special conditions, however I'm not aware of this being something you can do right now with off-the-shelf software and hardware. And while rCuda exists its only free for academic use, and Cycles would need to be modified to support it.